The most common Quake-style terminal in Gnome seem to be Guake and Tilda, but they can't split to show several shells in single tab like Yakuake can. Is there any alternative which can do so?

Try Guake with tmux to get the splitting feature.

For Ubuntu 14.04

Terra can be made to run on Ubuntu 14.04. See this answer for details

For Ubuntu 13.04 and older

Alternatively there is a new experimental project called Terra.

Terra is a GTK+3.0 based terminal emulator with useful user interface,
it also supports multiple terminals with splitting screen horizontally
or vertically.

Quick installation:

sudo add-apt-repository ppa:ozcanesen/terra-terminal

sudo apt-get update

sudo apt-get install terra

For more information check out the WebUpd8 article.

You can write a small script to make any window bring to the front. Though it is not sliding down from top like in quake it serves the purpose. I'm using terminator as my grid terminal since its very powerful.

The script I'm using for this is given below. So first install terminator and wmctrl then put this script where you keep your scripts and add a shortcut key (eg: Ctrl+`) and your done.

Now when you press Ctrl+` terminator comes to the front and press the same once more, it will go to the back of the other windows.

#!/bin/bash

TM_STATE=/tmp/tm_stat

WIN=$( wmctrl -lGx | grep -i terminator | awk '{print $1}' );

if [[ $WIN == "" ]]

then

   terminator&

   exit 0

else

   if [[ -e $TM_STATE ]]

   then

      wmctrl -i -r $WIN -b remove,below

      wmctrl -i -r $WIN -b add,above

      #wmctrl -i -r $WIN -b remove,shaded

      #wmctrl -i -a $WIN 

      rm $TM_STATE

   else

      wmctrl -i -r $WIN -b remove,above

      wmctrl -i -r $WIN -b add,below

      #wmctrl -i -r $WIN -b add,shaded

      touch $TM_STATE

   fi

fi

Byobu

I use (now on 16.04) Guake with Byobu as shell interpreter, which by default use tmux (probably better than screen).

Three steps

1. Install: sudo apt-get install byobu (no PPAs needed).


2. Add it to available shells: which byobu | tee -a /etc/shells, as I told in this Guake Github issue.


3. On Guake preferences (guake-prefs) choose Byobu as the default interpreter:
   
   


4. 
   

   Optional: Hide tab bar, since you will use Byobu for that:

   
   
   

   

   
   


5. If a shortcut doesn't work try disabling Guake ones that might interfere (in my case was Ctrl+F2 for vertical split):
   
   

Other suggestions

1. Learn shortcuts with Shift+F1 or this excellent screencast.


2. Learn available byobu terminal commands with apropos byobu
   


3. To use fn keys on Midnight Commander use Alt+Nº or Shift+F12 to disable byobu F-keys.


4. 
   Tilix quake mode seems a acceptable alternative to Guake.

For Xenial users do this. It works great with terminator so far.

This will run/show/hide when using keyboard shortcut

I had F12 mapped to show/hide Guake for a while now but wanted terminal panes.

sudo apt update && sudo apt install xdotool wmctrl

cd ~ && touch terminator_show_hide.sh && sudo chmod +x terminator_show_hide.sh

Paste this in the file:

#!/bin/bash                                                                                                            

#

# This script does this:

# launch an app if it isn't launched yet,

# focus the app if it is launched but not focused,

# minimize the app if it is focused.

#

# by desgua - 2012/04/29

# modified by olds22 - 2012/09/16

#  - customized to accept a parameter

#  - made special exception to get it working with terminator





# First let's check if the needed tools are installed:



tool1=$(which xdotool)

tool2=$(which wmctrl)



if [ -z $tool1 ]; then

  echo "Xdotool is needed, do you want to install it now? [Y/n]"

  read a

  if [[ $a == "Y" || $a == "y" || $a = "" ]]; then

    sudo apt-get install xdotool

  else

    echo "Exiting then..."

    exit 1

  fi

fi



if [ -z $tool2 ]; then

  echo "Wmctrl is needed, do you want to install it now? [Y/n]"

  read a

  if [[ $a == "Y" || $a == "y" || $a = "" ]]; then

    sudo apt-get install wmctrl

  else

    echo "Exiting then..."

    exit 1

  fi

fi





# check if we're trying to use an app that needs a special process name

# (because it runs multiple processes and/or under a different name)

app=$1

if [[ $app == terminator ]]; then

  process_name=usr/bin/terminator

else

  process_name=$app

fi



# Check if the app is running (in this case $process_name)



#pid=$(pidof $process_name) # pidof didn't work for terminator

pid=$(pgrep -f $process_name)



# If it isn't launched, then launch



if [ -z $pid ]; then

  $app



else



  # If it is launched then check if it is focused



  foc=$(xdotool getactivewindow getwindowpid)



  if [[ $pid == $foc ]]; then



    # if it is focused, then minimize

    xdotool getactivewindow windowminimize

  else

    # if it isn't focused then get focus

    wmctrl -x -R $app

  fi

fi



exit 0

Then drop Guake map, if replacing the same shortcut like I was.

Open System Settings GUI -> Keyboard -> Shortcuts -> Custom Shortcuts

Click + and add this to command line:
/home/you/terminator_show_hide.sh terminator

Then map the key right there and you should be good to go.

This is slightly modified version of https://askubuntu.com/a/189603/597130

I didn't have the bin folder mentioned and it wouldn't fire from home/me/.local/bin but when I moved it to /home/me/ it worked instantly.

Now I have the best of both worlds, Guake Show/Hide & PANES!!
FYI: I'm putting this info here because I found this post on first search. I found the other post after digging a little wider hole.